Source code for openquake.hazardlib.gsim.usgs_ceus_2019

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2022 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:`NGAEastUSGSGMPE`
"""
import os
import numpy as np
from scipy.interpolate import interp1d
from openquake.hazardlib import const
from openquake.hazardlib.gsim.base import CoeffsTable, add_alias
from openquake.hazardlib.gsim.nga_east import (
    ITPL, NGAEastGMPE, get_mean_amp, get_site_amplification_sigma)
from openquake.hazardlib.gsim.gmpe_table import _get_mean

# Coefficients for EPRI sigma model taken from Table 5.5 of Goulet et al.
# (2017)
COEFFS_USGS_SIGMA_EPRI = CoeffsTable(sa_damping=5, table="""\
imt     tau_M5   phi_M5   tau_M6   phi_M6   tau_M7   phi_M7
pgv     0.3925   0.5979   0.3612   0.5218   0.3502   0.5090
pga     0.4320   0.6269   0.3779   0.5168   0.3525   0.5039
0.010   0.4320   0.6269   0.3779   0.5168   0.3525   0.5039
0.020   0.4710   0.6682   0.4385   0.5588   0.4138   0.5462
0.030   0.4710   0.6682   0.4385   0.5588   0.4138   0.5462
0.050   0.4710   0.6682   0.4385   0.5588   0.4138   0.5462
0.075   0.4710   0.6682   0.4385   0.5588   0.4138   0.5462
0.100   0.4710   0.6682   0.4385   0.5588   0.4138   0.5462
0.150   0.4433   0.6693   0.4130   0.5631   0.3886   0.5506
0.200   0.4216   0.6691   0.3822   0.5689   0.3579   0.5566
0.250   0.4150   0.6646   0.3669   0.5717   0.3427   0.5597
0.300   0.4106   0.6623   0.3543   0.5846   0.3302   0.5727
0.400   0.4088   0.6562   0.3416   0.5997   0.3176   0.5882
0.500   0.4175   0.6526   0.3456   0.6125   0.3217   0.6015
0.750   0.4439   0.6375   0.3732   0.6271   0.3494   0.6187
1.000   0.4620   0.6219   0.3887   0.6283   0.3650   0.6227
1.500   0.4774   0.5957   0.4055   0.6198   0.3819   0.6187
2.000   0.4809   0.5860   0.4098   0.6167   0.3863   0.6167
3.000   0.4862   0.5813   0.4186   0.6098   0.3952   0.6098
4.000   0.4904   0.5726   0.4144   0.6003   0.3910   0.6003
5.000   0.4899   0.5651   0.4182   0.5986   0.3949   0.5986
7.500   0.4803   0.5502   0.4067   0.5982   0.3835   0.5982
10.00   0.4666   0.5389   0.3993   0.5885   0.3761   0.5885
""")


COEFFS_USGS_SIGMA_PANEL = CoeffsTable(sa_damping=5, table="""\
imt         t1       t2       t3       t4     ss_a     ss_b    s2s1    s2s2
pgv     0.3633   0.3532   0.3340   0.3136   0.4985   0.3548   0.487   0.458
pga     0.4436   0.4169   0.3736   0.3415   0.5423   0.3439   0.533   0.566
0.010   0.4436   0.4169   0.3736   0.3415   0.5423   0.3439   0.533   0.566
0.020   0.4436   0.4169   0.3736   0.3415   0.5410   0.3438   0.537   0.577
0.030   0.4436   0.4169   0.3736   0.3415   0.5397   0.3437   0.542   0.598
0.050   0.4436   0.4169   0.3736   0.3415   0.5371   0.3435   0.583   0.653
0.075   0.4436   0.4169   0.3736   0.3415   0.5339   0.3433   0.619   0.633
0.100   0.4436   0.4169   0.3736   0.3415   0.5308   0.3431   0.623   0.590
0.150   0.4436   0.4169   0.3736   0.3415   0.5247   0.3466   0.603   0.532
0.200   0.4436   0.4169   0.3736   0.3415   0.5189   0.3585   0.578   0.461
0.250   0.4436   0.4169   0.3736   0.3415   0.5132   0.3694   0.554   0.396
0.300   0.4436   0.4169   0.3736   0.3415   0.5077   0.3808   0.527   0.373
0.400   0.4436   0.4169   0.3736   0.3415   0.4973   0.4004   0.491   0.339
0.500   0.4436   0.4169   0.3736   0.3415   0.4875   0.4109   0.472   0.305
0.750   0.4436   0.4169   0.3736   0.3415   0.4658   0.4218   0.432   0.273
1.000   0.4436   0.4169   0.3736   0.3415   0.4475   0.4201   0.431   0.257
1.500   0.4436   0.4169   0.3736   0.3415   0.4188   0.4097   0.424   0.247
2.000   0.4436   0.4169   0.3736   0.3415   0.3984   0.3986   0.423   0.239
3.000   0.4436   0.4169   0.3736   0.3415   0.3733   0.3734   0.418   0.230
4.000   0.4436   0.4169   0.3736   0.3415   0.3604   0.3604   0.412   0.221
5.000   0.4436   0.4169   0.3736   0.3415   0.3538   0.3537   0.404   0.214
7.500   0.4436   0.4169   0.3736   0.3415   0.3482   0.3481   0.378   0.201
10.00   0.4436   0.4169   0.3736   0.3415   0.3472   0.3471   0.319   0.193
""")


[docs]def get_epri_tau_phi(imt, mag): """ Returns the inter-event (tau) and intra_event standard deviation (phi) according to the updated EPRI (2013) model""" C = COEFFS_USGS_SIGMA_EPRI[imt] if mag <= 5.0: tau = C["tau_M5"] phi = C["phi_M5"] elif mag <= 6.0: tau = ITPL(mag, C["tau_M6"], C["tau_M5"], 5.0, 1.0) phi = ITPL(mag, C["phi_M6"], C["phi_M5"], 5.0, 1.0) elif mag <= 7.0: tau = ITPL(mag, C["tau_M7"], C["tau_M6"], 6.0, 1.0) phi = ITPL(mag, C["phi_M7"], C["phi_M6"], 6.0, 1.0) else: tau = C["tau_M7"] phi = C["phi_M7"] return tau, phi
[docs]def get_panel_tau_phi(imt, mag): """ Returns the inter-event (tau) and intra_event standard deviation (phi) according to the USGS Sigma Panel recommendations """ C = COEFFS_USGS_SIGMA_PANEL[imt] # Get tau if mag <= 4.5: tau = C["t1"] elif mag <= 5.0: tau = ITPL(mag, C["t2"], C["t1"], 4.5, 0.5) elif mag <= 5.5: tau = ITPL(mag, C["t3"], C["t2"], 5.0, 0.5) elif mag <= 6.5: tau = ITPL(mag, C["t4"], C["t3"], 5.5, 1.0) else: tau = C["t4"] # Get phi if mag <= 5.0: phi = C["ss_a"] elif mag <= 6.5: phi = ITPL(mag, C["ss_b"], C["ss_a"], 5.0, 1.5) else: phi = C["ss_b"] return tau, phi
[docs]def get_stewart_2019_phis2s(imt, vs30): """ Returns the phis2s model of Stewart et al. (2019) """ v_1 = 1200. v_2 = 1500. C = COEFFS_USGS_SIGMA_PANEL[imt] phis2s = C["s2s1"] + np.zeros(vs30.shape) idx = vs30 > v_2 phis2s[idx] = C["s2s2"] idx = np.logical_and(vs30 > v_1, vs30 <= v_2) if np.any(idx): phis2s[idx] = C["s2s1"] - ((C["s2s1"] - C["s2s2"]) / (v_2 - v_1)) *\ (vs30[idx] - v_1) return phis2s
@_get_mean.add("usgs") def _get_mean(kind, distance_type, data, dctx, ctx): """ Returns the mean intensity measure level from the tables applying log-log interpolation of the IML with distance (contrast with the linear interpolation applied in usual GMPE tables) :param data: The intensity measure level vector for the given magnitude and IMT :param key: The distance type :param distances: The distance vector for the given magnitude and IMT """ # For values outside of the interpolation range use -999. to ensure # value is identifiable and outside of potential real values # For extremely short distance (rrup = 0) use an arbitrarily small # distance measure (1.0E-5 used by US NSHMP code) ctx[ctx < 1.0E-5] = 1.0E-5 interpolator_mean = interp1d(np.log10(ctx), np.log(data), bounds_error=False, fill_value=-999.) mean = np.exp(interpolator_mean(np.log10(getattr(dctx, distance_type)))) # For those distances less than or equal to the shortest distance # extrapolate the shortest distance value mean[getattr(dctx, distance_type) <= ctx[0]] = data[0] # For those distances significantly greater than the furthest distance # set to 1E-20. mean[getattr(dctx, distance_type) > (ctx[-1] + 1.0E-3)] = 1E-20 # If any distance is between the final distance and a margin of 0.001 # km then assign to smallest distance mean[mean < -1.] = data[-1] return mean def _get_stddevs(sigma_model, ctx, imt): """ Returns the standard deviations according to the choice of aleatory uncertainty model. Note that for compatibility with the US NSHMP code a weighted sum of the two aleatory uncertainty models is used, with the EPRI model assigned a weight of 0.8 and the PANEL model 0.2. """ if sigma_model in ("EPRI", "COLLAPSED"): # EPRI recommended aleatory uncertainty model tau_epri, phi_epri = get_epri_tau_phi(imt, ctx.mag) if sigma_model in ("PANEL", "COLLAPSED"): # Panel recommended model tau_panel, phi0_panel = get_panel_tau_phi(imt, ctx.mag) phis2s = get_stewart_2019_phis2s(imt, ctx.vs30) phi_panel = np.sqrt(phi0_panel ** 2. + phis2s ** 2.) if sigma_model == "EPRI": tau = tau_epri phi = phi_epri sigma = np.sqrt(tau ** 2. + phi ** 2.) elif sigma_model == "PANEL": tau = tau_panel phi = phi_panel sigma = np.sqrt(tau ** 2. + phi ** 2.) else: # Get the weighted sum of the two models sigma_epri = np.sqrt(tau_epri ** 2. + phi_epri ** 2.) sigma_panel = np.sqrt(tau_panel ** 2. + phi_panel ** 2.) sigma = 0.8 * sigma_epri + 0.2 * sigma_panel tau, phi = 0., 0. return [sigma, tau, phi]
[docs]class NGAEastUSGSGMPE(NGAEastGMPE): """ For the "core" NGA East set the table is provided in the code in a subdirectory fixed to the path of the present file. The GMPE table option is therefore no longer needed """ DEFINED_FOR_STANDARD_DEVIATION_TYPES = set((const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT)) gmpe_table = "" PATH = os.path.join(os.path.dirname(__file__), "usgs_nga_east_tables") kind = "usgs" def __init__(self, **kwargs): self.sigma_model = kwargs.get("sigma_model", "COLLAPSED") self.epistemic_site = kwargs.get("epistemic_site", True) if self.sigma_model not in ("EPRI", "PANEL", "COLLAPSED"): raise ValueError("USGS CEUS Sigma Model %s not supported" % self.sigma_model) if self.sigma_model == "COLLAPSED": # In the case of the collapsed model only the total standard # deviation can be defined self.DEFINED_FOR_STANDARD_DEVIATION_TYPES =\ set((const.StdDev.TOTAL,)) super().__init__(**kwargs)
[docs] def compute(self, ctx, imts, mean, sig, tau, phi): """ Returns the mean and standard deviations """ for m, imt in enumerate(imts): imean, site_amp, pga_r = get_mean_amp(self, ctx, imt) # Get the coefficients for the IMT C_LIN = self.COEFFS_LINEAR[imt] C_F760 = self.COEFFS_F760[imt] C_NL = self.COEFFS_NONLINEAR[imt] # Get collapsed amplification model for -sigma, 0, +sigma # with weights of 0.185, 0.63, 0.185 respectively if self.epistemic_site: f_rk = np.log((np.exp(pga_r) + C_NL["f3"]) / C_NL["f3"]) site_amp_sigma = get_site_amplification_sigma( self, ctx, f_rk, C_LIN, C_F760, C_NL) mean[m] = np.log( 0.185 * (np.exp(imean - site_amp_sigma)) + 0.63 * np.exp(imean) + 0.185 * np.exp(imean + site_amp_sigma)) else: mean[m] = imean # Get standard deviation model sig[m], tau[m], phi[m] = _get_stddevs( self.sigma_model, ctx, imt)
lines = '''\ NGAEastUSGSSeedSP15 SP15 NGAEastUSGSSeed1CCSP 1CCSP NGAEastUSGSSeed2CVSP 2CVSP NGAEastUSGSSeed1CVSP 1CVSP NGAEastUSGSSeed2CCSP 2CCSP NGAEastUSGSSeedGraizer Graizer NGAEastUSGSSeedB_ab95 B_ab95 NGAEastUSGSSeedB_bca10d B_bca10d NGAEastUSGSSeedB_sgd02 B_sgd02 NGAEastUSGSSeedB_a04 B_a04 NGAEastUSGSSeedB_bs11 B_bs11 NGAEastUSGSSeedB_ab14 B_ab14 NGAEastUSGSSeedHA15 HA15 NGAEastUSGSSeedPEER_EX PEER_EX NGAEastUSGSSeedPEER_GP PEER_GP NGAEastUSGSSeedGraizer16 Graizer16 NGAEastUSGSSeedGraizer17 Graizer17 NGAEastUSGSSeedFrankel Frankel NGAEastUSGSSeedYA15 YA15 NGAEastUSGSSeedPZCT15_M1SS PZCT15_M1SS NGAEastUSGSSeedPZCT15_M2ES PZCT15_M2ES NGAEastUSGSSammons1 usgs_1 NGAEastUSGSSammons2 usgs_2 NGAEastUSGSSammons3 usgs_3 NGAEastUSGSSammons4 usgs_4 NGAEastUSGSSammons5 usgs_5 NGAEastUSGSSammons6 usgs_6 NGAEastUSGSSammons7 usgs_7 NGAEastUSGSSammons8 usgs_8 NGAEastUSGSSammons9 usgs_9 NGAEastUSGSSammons10 usgs_10 NGAEastUSGSSammons11 usgs_11 NGAEastUSGSSammons12 usgs_12 NGAEastUSGSSammons13 usgs_13 NGAEastUSGSSammons14 usgs_14 NGAEastUSGSSammons15 usgs_15 NGAEastUSGSSammons16 usgs_16 NGAEastUSGSSammons17 usgs_17'''.splitlines() for line in lines: alias, key = line.split() add_alias(alias, NGAEastUSGSGMPE, gmpe_table=f"nga_east_{key}.hdf5")